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Structural Mechanics

Solve linear static, dynamic, and modal analysis problems

Navier partial differential equations describe the displacement field
as a function of body forces and structural properties of the material.
Knowing the displacement field, you can calculate the strain and stress fields:

(λ+μ)∇(∇⋅u)+μ∇2u+f=ρ∂2u∂t2

Here, vector u is the displacement,
ρ is the mass density, μ
is the shear modulus, λ is the Lame modulus of the
material, and f is a vector of volume
forces. The shear modulus and Lame modulus can be expressed via the
Young's (elastic) modulus E and the Poisson's ratio
ν:

μ=E2(1+ν),λ=νE(1+ν)(1−2ν),f=(fxfy)

A typical programmatic workflow for solving a linear elasticity
problem includes these steps:

Create a special structural analysis container for a solid
(3-D), plane stress, or plane strain model.

Define 2-D or 3-D geometry and mesh it.

Assign structural properties of the material, such as
Young's modulus, Poisson's ratio, and mass density.

For modal analysis problems, use the same steps for creating a model
and specifying materials and boundary constraints. In this case, the
solver finds natural frequencies and mode shapes of a structure.

For plane stress and plane strain problems, you also can use the PDE
Modeler app. The app includes geometry creation and preset modes for
applications.